There is no difference in how fast the players and the ball move across the pitch on the two modes.
The option is thre because in Japan and America NTSC tvs update at a rate of 60 times per second. In Europe the defualt is 50.
When playing a console game, the developers set the game to wait until the TV is finished putting each frame onto the screen before allowing it to continue onto the next frame. So, on a standard European tv the game only updates 50 times and in NTSC countries it updates 60 times per second. Newer PAL tvs also support either NTSC itself or a similar system called PAL60 which updates 60 times also.
That's the reason why 50 and 60htz modes exists, now here's the difference they make.
Games do not update their input every fram, most games do it every 10 frames or there abouts, so you will have a more fluid control system if you are updating 6 times a frame rather than 5, it just makes the game a little more responsive. 60 updates rather than 5 also give smoother animations. So the players move at the same speed but their legs and arms are updated more often on 6o hrtz mode meaning it looks a lot nicer.
So, for the increased responsiveness and fluiditi you get, you have to pay a price. Updating 60 times in one second means that you have only 0.01666 seconds to make all of the needed calculations to update that frame. Updating 50 times a second gives you 0.02 secs per frame.
Slow down occurs when the frame takes longer to process than it takes the TV to update becasue the tv will update whether the PS2 is ready or not and it the PS2 hasn't updated a new frame the old frame will be displayed making the screen appear to stick. The physics system will continue to update though so eventually either the game slows down to catch up with the animations or you just miss out the frames entirely or a mixture of both occurs.
So obviously the Pro Evo game needs between 0.01666 and 0.02 secs to complete a ful frame meaning that 50hrtz has no slowdown and 60htrz does. The only way konami could fix this would be to make the physics less realistic, remove some of the AI calculations or make the graphics and animations look worse. None of which are a good idea.
So the bottom line is that in Europe at least we have a choice of whether we want to accept the slowdown or not and in NTSC countries they have to use 60htz or nothing.